A government crackdown on tax evasion in overseas havens is expected to raise £10bn in this parliament, far more than previous forecasts.

The unexpected windfall follows negotiations between national governments and the British tax authorities, Treasury officials disclosed yesterday.

The Treasury had only budgeted to raise £1bn across the parliament, mainly from an agreement with Liechtenstein. But George Osborne, the chancellor, is now expecting to raise £2bn to £3bn from secret bank accounts in the mini-state alone.

Officials said a further £3bn was expected to be raised from Swiss bank accounts after an agreement with tax authorities there, signed 10 days ago, to push forward on a deal. There is thought to be up to £125bn stashed away in Swiss bank accounts by British citizens.

The Treasury said three further tax havens had asked to open negotiations on information disclosure, the method by which Revenue & Customs is locating billions the British super-rich have salted away and then taxing accounts and demanding back payment of unpaid tax.

Officials declined to identify the three countries amid concerns money might be shifted out before any agreements can be signed. Each of the havens, one of which is in the Caribbean, was expected to raise a further £1bn. The officials said that the Cayman Islands, one of the biggest offshore tax havens, was not among them.

The havens have been under pressure to reach a deal with Britain. An information disclosure agreement allows them to be taken off the "greylist" of non-compliant countries drawn up by the Organisation for Economic Co-operation and Development.

Gordon Brown raised the issue of tax evasion repeatedly at meetings of the G8 and the G20, but progress has been painfully slow until the past two years.

The Treasury said the funds raised will be used to pay down the £155bn deficit, but were unable to say at what point in the parliament the unexpected windfall will land.

A Treasury official said: "These agreements, by allowing us to get information from tax havens, means British tax authorities are gaining complete access to details of bank accounts. We are discovering much more than we had assumed we would."

The Treasury said it could not predict whether individuals would be prosecuted as a result of the discoveries, but said in clear cases of tax evasion it is likely to lead to court action.

The cash is being raised through a mixture of imposing tax on accounts and by demanding back payments of unpaid tax that should have been paid to the Treasury.

Osborne said: "We are in this together and that includes those who try to evade tax. We are in the process of striking a deal with Switzerland and more will follow. This will raise many billions of pounds that the previous government failed to do. This is tough but fair."

In Labour's last budget, the then chancellor Alistair Darling said he was starting talks on a tax agreement with Dominica, Grenada and Belize, the home of Lord Ashcroft, the Tory donor.